Pilot Study of Bortezomib, Bendamustine and Rituximab on Non-Hodgkin's Lymphoma

Inclusion Criteria: * Voluntary written informed consent before performance of any study-specific procedure not part of routine medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Female subject is either post-menopausal or surgically sterilized or willing to use acceptable method of birth control for duration of study. * Male subject agrees to use acceptable method for contraception for duration of study. * Histologically-confirmed indolent or mantle cell lymphoma, utilizing the World Health Organization (WHO) classification. The biopsy must fulfill one of the following criteria: * Follicular lymphoma, grades 1-3 * Marginal zone lymphoma * Small lymphocytic lymphoma (circulating lymphocyte count must be \< 5,000) * Lymphoplasmacytic lymphoma * Mantle cell lymphoma \[confirmed by cyclin D1+ or FISH for t(11;14)\] * Age ≥ 18 years * Must have received at least one prior chemotherapy regimen for lymphoma. Patients treated only with antibody therapy or only with radiation therapy are not eligible. * Zubrod performance status ≤ 3 * Patients must have measurable disease or an indication to receive additional therapy Exclusion Criteria: * Patient has platelet count of ≤75,000/mm\^3 within 14 days before enrollment. * Patient has absolute neutrophil count of \< 1,000/mm\^3 within 14 days before enrollment. * Patient has calculated or measured creatinine clearance of \<30 mL/minute within 14 days before enrollment. * Patient has ≥ Grade 2 peripheral neuropathy within 14 days before enrollment. * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at Screening has to be documented by the investigator as not medically relevant. * Patient has hypersensitivity to boron or mannitol * Female subject is pregnant or breast-feeding. Confirmation subject is not pregnant must be established by negative serum ß-human chorionic gonadotropin (ß-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for post-menopausal or surgically sterilized women. * Patient has received chemotherapy or antibody therapy within 28 days before enrollment * Serious medical or psychiatric illness likely to interfere with participation in this clinical study. * Patient has received other investigational drugs with 14 days before enrollment * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy. * Prior exposure to bendamustine * Prior exposure to bortezomib if Time to Progression (TTP) after bortezomib containing regimen was \< 6 months. If TTP after bortezomib containing regimen was \> 6 months, then patient is allowed to enroll on the study. * Patient has concomitant active malignancy requiring therapy * Patient is known to be HIV positive (test result not required for enrollment). * History of solid organ transplantation, or post transplant lymphoproliferative disorder * Patient has history of allogeneic stem cell transplantation. * Patient has history of autologous stem cell transplantation or radioimmunotherapy within the previous 4 months. * Patient has received any other investigational drugs within 14 days prior to enrollment * History of, or clinically apparent CNS lymphoma * Any clinically significant abnormality in screening blood chemistry, hematology, or urinalysis results that, in the judgment of the investigator, would impede adequate evaluation of adverse events and/or response to treatment, or that requires aggressive intervention